Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
492 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66629 | C2 | semidirect |
| 3. C2×C3×C4×Dic7 | C2 | semidirect |
| 4. C2×Dic3⋊Dic7 | C2 | semidirect |
| 5. C2×#66577 | C2 | semidirect |
| 8. #10620934 | C2 | direct (N × H) |
| 17. #66629 | C22 | semidirect |
| 19. C3×C4×Dic7 | C22 | semidirect |
| 20. Dic3⋊Dic7 | C22 | semidirect |
| 21. #66577 | C22 | semidirect |
| 30. C2×C4×Dic7 | D3 | semidirect |
| 63. C4×Dic7 | C2×D3 | semidirect |
| 118. C2×C3×C7 | #126 | semidirect |
| 162. C3×C7 | C2×#126 | semidirect |
| 178. C2×C7 | #876 | semidirect |
| 213. C7 | C2×#876 | semidirect |
| 214. C2×C3 | #6442 | semidirect |
| 233. C3 | C2×#6442 | semidirect |
| 235. C2 | #10620934 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66629 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×#66577 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620934 | 2 |
| C2×#6442 | 3 |
| C2×#876 | 7 |